The nearby (d = 12 pc) M8 dwarf star TRAPPIST-1 (2MASS J23062928-0502285) hosts a compact system of at least seven exoplanets with sizes similar to Earth. Given its importance for testing planet formation and evolution theories, and for assessing the prospects for habitability among Earth-size exoplanets orbiting the most common type of star in the Galaxy, we present a comprehensive assessment of the age of this system. We collate empirical age constraints based on the color-absolute magnitude diagram, average density, lithium absorption, surface gravity features, metallicity, kinematics, rotation, and magnetic activity; and conclude that TRAPPIST-1 is a transitional thin/thick disk star with an age of 7.6 ± 2.2 Gyr. The star's color-magnitude position indicates that it is slightly metal-rich, which is consistent with the previously reported near-infrared spectroscopic metallicity; and it has a radius (R=0.121 ± 0.003 R☉) that is larger by 8%-14% than the predictions of solar-metallicity evolutionary models. We discuss some implications of the old age of this system with regard to the stability and habitability of its planets.